Subgroups — C₇×C₃⋊D₁₀₅ #17984414

Order 4410.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅×C₇²	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×D₁₀₅	—	3	4	no	maximal
3	C₇×C₃⋊D₂₁	—	5	1	no	maximal, Hall
4	C₃×C₅×C₇²	D₃	1	4	yes	complemented
5	C₃⋊D₁₀₅	C₇	1	1	yes	maximal, characteristic, direct product factor
6	C₇×C₃⋊D₁₅	—	7	1	no	maximal
7	C₇×D₃₅	—	9	1	no	Hall
8	C₃²×C₇²	D₅	1	1	yes	characteristic, complemented, Hall
9	C₃²×C₅×C₇	—	2	3	no	—
10	C₃²×C₅×C₇	D₇	1	1	yes	characteristic, complemented
11	C₃²×C₅×C₇	C₂×C₇	1	1	yes	characteristic, complemented
12	C₇×D₂₁	—	15	4	no	—
13	C₅×C₇²	C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
14	D₁₀₅	—	3	4	no	—
15	C₇×D₁₅	—	21	4	no	—
16	C₃×C₇²	D₁₅	1	4	yes	complemented
17	C₃⋊D₂₁	—	5	1	no	—
18	C₇×C₃⋊D₃	—	35	1	no	—
19	C₃×C₅×C₇	—	2	12	no	—
20	C₃×C₅×C₇	D₃×C₇	1	4	yes	complemented
21	C₃×C₅×C₇	D₂₁	1	4	yes	complemented
22	C₇×D₇	—	45	1	no	Hall
23	C₃⋊D₁₅	—	7	1	no	Hall
24	D₃₅	—	9	1	no	—
25	C₇×D₅	—	63	1	no	—
26	C₃²×C₇	—	2	3	no	—
27	C₃²×C₇	C₇×D₅	1	1	yes	characteristic, complemented
28	C₃²×C₇	D₃₅	1	1	yes	characteristic, complemented
29	C₇²	C₃⋊D₁₅	1	1	yes	characteristic, complemented, Sylow
30	C₃²×C₅	C₇×D₇	1	1	yes	characteristic, complemented, Hall
31	D₂₁	—	15	4	no	—
32	D₃×C₇	—	105	4	no	—
33	C₅×C₇	—	2	3	no	—
34	C₅×C₇	C₇×C₃⋊D₃	1	1	yes	characteristic, complemented
35	C₅×C₇	C₃⋊D₂₁	1	1	yes	characteristic, complemented
36	D₁₅	—	21	4	no	—
37	C₃×C₇	—	2	12	no	—
38	C₃×C₇	C₇×D₁₅	1	4	yes	complemented
39	C₃×C₇	D₁₀₅	1	4	yes	complemented
40	C₃⋊D₃	—	35	1	no	Hall
41	C₃×C₅	C₇×D₂₁	1	4	yes	complemented
42	C₂×C₇	—	315	1	no	—
43	D₇	—	45	1	no	—
44	D₅	—	63	1	no	Hall
45	C₃²	C₇×D₃₅	1	1	yes	characteristic, complemented, Sylow
46	C₇	—	2	3	no	—
47	C₇	C₇×C₃⋊D₁₅	1	1	yes	characteristic, complemented
48	C₇	C₃⋊D₁₀₅	1	1	yes	characteristic, direct product factor
49	D₃	—	105	4	no	—
50	C₅	C₇×C₃⋊D₂₁	1	1	yes	characteristic, complemented, Sylow
51	C₃	C₇×D₁₀₅	1	4	yes	complemented
52	C₂	—	315	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇	C₃⋊D₁₀₅
commutator, cosocle, hypocenter	C₃²×C₅×C₇	C₂×C₇
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₇²	C₂
LCS	G ▷ C₃²×C₅×C₇
UCS	C₁ ◁ C₇

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₃²×C₅×C₇²	C₂	semidirect
4. C₃×C₅×C₇²	D₃	semidirect
5. C₃⋊D₁₀₅	C₇	direct (N × H)
8. C₃²×C₇²	D₅	semidirect
10. C₃²×C₅×C₇	D₇	semidirect
11. C₃²×C₅×C₇	C₂×C₇	semidirect
13. C₅×C₇²	C₃⋊D₃	semidirect
16. C₃×C₇²	D₁₅	semidirect
20. C₃×C₅×C₇	D₃×C₇	semidirect
21. C₃×C₅×C₇	D₂₁	semidirect
27. C₃²×C₇	C₇×D₅	semidirect
28. C₃²×C₇	D₃₅	semidirect
29. C₇²	C₃⋊D₁₅	semidirect
30. C₃²×C₅	C₇×D₇	semidirect
34. C₅×C₇	C₇×C₃⋊D₃	semidirect
35. C₅×C₇	C₃⋊D₂₁	semidirect
38. C₃×C₇	C₇×D₁₅	semidirect
39. C₃×C₇	D₁₀₅	semidirect
41. C₃×C₅	C₇×D₂₁	semidirect
45. C₃²	C₇×D₃₅	semidirect
47. C₇	C₇×C₃⋊D₁₅	semidirect
48. C₇	C₃⋊D₁₀₅	direct (N × H)
50. C₅	C₇×C₃⋊D₂₁	semidirect
51. C₃	C₇×D₁₀₅	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃²×C₅×C₇²	2
C₇×D₁₀₅	3
C₇×C₃⋊D₂₁	5
C₃⋊D₁₀₅	7
C₇×C₃⋊D₁₅	7

Subgroups — C7×C3⋊D105 #17984414

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×C₃⋊D₁₀₅ #17984414